Differential geometry of foliations
نویسندگان
چکیده
منابع مشابه
Noncommutative Geometry of Foliations
We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.
متن کاملOn the k-nullity foliations in Finsler geometry
Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...
متن کاملAdiabatic limits and spectral geometry of foliations
Let (M, F) be a closed foliated manifold, dimM = n, dimF = p, p+q = n, equipped with a Riemannian metric gM . We assume that the foliation F is Riemannian, and the metric gM is bundle-like. Let F = TF be the integrable distribution of tangent p-planes to F , and H = F⊥ be the orthogonal complement to F . The decomposition of TM into a direct sum, TM = F ⊕ H , induces a decomposition of the metr...
متن کاملContact Geometry of One Dimensional Holomorphic Foliations
ABSTRACT. Let V be a real hypersurface of class Ck, k ≥ 3, in a complex manifold M of complex dimension n + 1, HT (V ) the holomorphic tangent bundle to V giving the induced CR structure on V . Let θ be a contact form for (V,HT (V )), ξ0 the Reeb vector field determined by θ and assume that ξ0 is of class Ck. In this paper we prove the following theorem (cf. Theorem 4.1): if the integral curves...
متن کاملNoncommutative spectral geometry of Riemannian foliations
According to [9, 8], the initial datum of noncommutative differential geometry is a spectral triple (A,H, D) (see Section 3.1 for the definition), which provides a description of the corresponding geometrical space in terms of spectral data of geometrical operators on this space. The purpose of this paper is to construct spectral triples given by transversally elliptic operators with respect to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1985
ISSN: 0001-8708
DOI: 10.1016/0001-8708(85)90109-4